1. Introduction
The ultrasonic motor (USM) is an actuator that converts the stator’s vibration excited by the inverse piezoelectric effect into continuous rotor motion through friction [
1]. The USM has wide applications in the fields of robotics [
2,
3], precision positioning systems [
4], medical systems [
5,
6], and aerospace vehicles [
7] due to advantages such as fast response, small size, and negligible electromagnetic interference.
In recent years, several studies have focused on miniaturized USM fabricated by wafer-scale microelectromechanical system (MEMS) techniques to reduce manufacturing cost, improve manufacturing precision, and enhance the capabilities of system-level integration. Rudy et al. proposed a MEMS USM made of a silicon layer and a thin lead zirconate titanate (PZT) film for the first time [
8,
9]. Zhou et al. used the saddle points of the modal shape to improve the quality factor of the MEMS USM [
10,
11]. Ran et al. established a three-dimensional contact model for the MEMS USM [
12]. Zhao et al. proposed a MEMS USM with a thick PZT film to improve performance [
13]. Hareesh et al. proposed a MEMS USM using the bulk PZT wafer to suppress the residual stress [
14]. He et al. studied the traveling wave distortion in MEMS USM to improve performance [
15].
Though the prototype of MEMS USM has been successfully fabricated, it is still a challenge to apply it in high-precision systems, such as precision positioning systems, because it is difficult to monitor the rotation precisely on a miniaturized scale. Optical and capacitive rotation-measuring systems are widely adopted for conventional macroscale motors. However, the optical rotation-measuring system is infeasible for the MEMS USM because the high-precision fabrication of a large number of gratings on a miniaturized scale is challenging, and a high-quality light source limits the size and cost [
16]. In our previous study, a capacitive rotation-measuring system was established for MEMS USM [
17]. However, the fabrication of the shielding layer for the parasitic capacitance is challenging and high-cost on a miniaturized scale [
17]. Additionally, the rotor’s out-of-plane movement also induces a significant error because the out-of-plane movement changes the capacitive gap [
17].
Compared to the optical and capacitive ones, the magnetic rotation-measuring system using tunneling magnetoresistance (TMR) sensors has the advantages of miniature size, high resolution, and low cost [
18]. This kind of rotation-measuring system has been widely applied to macroscale rotation. For instance, Muna et al. explored the optimal magnetic field of the magnetic rotation-measuring system using TMR sensors by finite element analysis to realize the high resolution [
19]. Bhaskarrao et al. proposed a TMR-based rotation-measuring system with a linearizing digital interface for shaft rotation [
20,
21]. Wang et al. presented TMR sensors from Multi Dimension Technology of China as a rotation-measuring element embedded into the permanent magnet synchronous motor [
18,
22].
Due to the advantage of miniature size, the TMR sensor has great potential for monitoring the rotation of miniaturized motors, such as the MEMS USM. However, there are no published reports so far. This study uses TMR sensors to establish a high-resolution rotation-measuring system for MEMS USM for the first time, which provides a feasible path to overcome the challenge of monitoring the rotation of miniaturized motors. Initially, the architecture and principle of the rotation-measuring system are described. Secondly, the finite element simulations are implemented to determine the miniaturized permanent magnet’s residual magnetization, dimensions, and TMR sensor position. Finally, the experiments are implemented, and the tested results are discussed.
2. Architecture and Principle of the Rotation-Measuring System
A schematic diagram for the rotation-measuring system is shown in
Figure 1. Firstly, the stator of the USM is mounted on the baseboard by adhesives. The miniaturized stator has a diameter as low as 4 mm. Then, an Iron rotor with a permanent magnet for angle detecting (PMAD) is placed on the stator in the out-of-plane direction, and an Aluminum shaft constrains its in-plane motions, as shown in
Figure 1a. The PMAD is made of Neodymium Iron Boron and magnetized radially, as shown in
Figure 1b. A TMR sensor is placed on the head of the PMAD, and its center is aligned with that of the PMAD. A preload for generating frictional driving force between the stator and rotor is necessary. In this work, the preload is produced by the attraction between the Iron rotor and a permanent magnet under the stator. The permanent magnet for preload (PMP) is vertical magnetization and also made of Neodymium Iron Boron.
A step-by-step block diagram describing the working principle of the rotation-measuring system is shown in
Figure 1c. When the driving voltages are applied, the traveling wave is excited on the stator by the inverse piezoelectric effect. Then, the traveling wave vibration is converted into continuous rotation of the rotor and PMAD through friction. The PMAD is magnetized radially, so the rotation of PMAD changes the direction of the magnetic field passing through the TMR sensor, as shown in
Figure 1b. The X and Y elements of the TMR sensor change their resistance depending on the direction of the magnetic field, and the Wheatstone bridges transform the resistance variation into voltages with Cos and Sin waveforms [
23]:
where
Vx and
Vy, respectively, refer to the voltages produced by the X and Y elements of the TMR sensor,
Vp represents the peak value, and
θ represents the rotational angle of the rotor. Finally, to yield the linear relationship between the output and rotational angle, the Cos and Sin voltages are input into the linearizing interface circuits to perform an inverse-trigonometric operation [
24], as shown in
Figure 2. Because the output of the inverse-trigonometric operation is 0°~360°, even as the rotational angle can continue to increase, the output will inevitably return to zero per 360° [
24]. The turning point is at the zero-position where the output of the TMR sensor is zero, i.e., the magnetic direction makes
Vx maximum and
Vy zero [
23].
3. Simulation of the Magnetic Field
The exact magnetic field in a compact space must be produced to satisfy the requirements of rotational measuring and preload. In this section, detailed finite element simulations of the magnetic field are implemented to determine the miniaturized permanent magnet’s residual magnetization, dimensions, and TMR sensor position.
This study employs the commercial finite element software COMSOL Multiphysics 6.1 to simulate the magnetic field [
25]. The diameters and thicknesses of the miniaturized permanent magnets and the rotor are listed in
Table 1. The distance from the PMP to the rotor is 800 µm. These dimensions are determined to make the motor compact. Additionally, the PMAD’s diameter is smaller than the Iron rotor’s diameter to shield its effect on the magnetic attraction between the Iron rotor and PMP. Otherwise, a moment could be generated on the rotor to result in an inhomogeneous preload between the rotor and stator. The relative permeability of the stator, shaft, and baseboard is close to that of air, so they are all replaced by the air in the simulation model. The magnetization of the PMP is 400 kA/m. The PMAD’s residual magnetization and the TMR sensor’s position are parameters determined by the finite element simulations.
The simulation results are shown in
Figure 3. The gap between the PMAD and rotor represents the space of adhesives. It can be seen from
Figure 3 that the magnetic field lines above the PMAD correspond to the radial direction, which ensures that the TMR sensor can sense the rotation of the rotor. A Cartesian coordinate system is established to describe the variation of the magnetic flux density in space, as shown in
Figure 3. The origin of the coordinate system is placed on the center of the top surface of the PMAD. The variation of the magnetic flux density is shown in
Figure 4. It can be seen that the magnetic flux density increases with an increase in the residual magnetization of the PMAD and decreases with an increase in the vertical coordinate. However, the horizontal coordinate has a negligible effect on magnetic flux density because the magnetic field lines correspond with the radial direction. The minimum at about −50 μm may be induced by the effect of PMP on the magnetic field. If there is no PMP under the stator, the magnetic flux density must be symmetric with the middle line, and an extreme point of magnetic flux density must be on the middle line. However, when a PMP is mounted under the rotor, the symmetry of the magnetic field must be broken. As a result, the location for the extreme point could change from the middle to other points, such as the point that
x = −50 μm.
The adopted TMR sensor in this paper comes from TDK Corporation and is labeled as TAD2141. TAD2141 is a digital sensor and has the advantages of high-accuracy angle sensing, miniature size, and low cost. The dimension of the TMR sensor is 5 mm × 4.4 mm × 1 mm, which is close to that of the MEMS USM. The magnetic flux density operating range for TAD2141 is from −20 mT to 80 mT [
23]. In
Figure 4c with the residual magnetization of 1700 kA/m, when the position of the TMR sensor varies from (0 mm, 0.8 mm) to (0 mm, 1.6 mm), the magnetic flux density varies from 55 mT to 25 mT. As a result, the requirement of the magnetic flux density for the angle detecting is satisfied.
According to the simulating results of the magnetic field, the preload provided by the magnetic attraction can be extracted by the built-in magnetic-force-calculation function of the COMSOL Multiphysics 6.1. The computed results of the preload are shown in
Figure 5a. It can be seen that the preload increases with the increase of the residual magnetization of the PMAD. The reason is that the Iron rotor is magnetized more intensely when the residual magnetization of the PMAD is higher. According to our previous testing, a preload of about 16 mN is optimal for motor performance. When the residual magnetization is 1700 kA/m, the preload is close to 16 mN, so the requirement for the preload is also satisfied.
Besides the force, a small torque also exists on the rotor, as shown in
Figure 5b. The small torque is induced by the interaction between the PMAD and PMP. According to the magnetic pole shown in
Figure 1, the N-pole of the PMAD must be repulsed by the PMP, while the S-pole must be attracted by the PMP. However, it can be seen from
Figure 5b that the torque is very small. For example, when the residual magnetization of the PMAD is 1700 kA/m, the resulting torque on the rotor is as low as 1.14 mN∙mm. Because the diameter of the rotor is 4 mm, the torque is equivalent to a pair of forces of 0.285 mN applied on the rotor, i.e., 1.14 mN∙mm = 2 × 0.285 mN × 2 mm. However, the preload applied on the rotor is 16 mN, which is much higher than 0.285 mN. Thus, this pair of forces has a very small effect on the preload. The reason is that the diameter of the PMAD is smaller than that of the Iron rotor, so interaction between the PMAD and PMP is shielded by the Iron rotor.
As a whole, the miniaturized PMAD with a residual magnetization of 1700 kA/m can satisfy both the requirements of the angle detecting and the preload.
4. Experimental Method
4.1. Fabrication and Assembly
The stator is fabricated by silicon-based wafer-level batch fabrication with film sputtering, as shown in
Figure 6. At first, the device layer of an SOI wafer is thinned to 25 μm (
Figure 6a). Then, a platinum layer is sputtered for the first electrode, followed by a 3 μm PZT film sputtered as the piezoelectric actuating layer; then, the second electrode is fabricated like the first one (
Figure 6b). By wet etching and ion beam etching, the PZT and metal layers are etched to pattern the electrodes, the same as those in literature [
10] (
Figure 6c).
Figure 6d shows the shaping of the annular stator by deep reactive ion etching (DRIE). Finally, the whole structure is released by DRIE on the backside (
Figure 6e).
After the release, the wafer is diced into the dies of the stator. Then, a die of the stator and a rotor are assembled into a complete motor, as shown in
Figure 7, and the wires are bonded to connect the pads of the stator and the baseboard. The PMAD is bonded on the rotor using adhesive. This manual bonding may induce a slight alignment error between the rotor and the PMAD. In future, the alignment mark can be made on the rotor to suppress the alignment error. Two manufactured motors are shown in
Figure 8. One of them is without the rotor to display the stator.
4.2. Testing Method
The testing architecture is shown in
Figure 9. Its main components include a MEMS USM, a TMR sensor, a printed circuit board, a high-precision servo motor (HPSM), a positioning stage, etc. A customized PMAD with a residual magnetization of 1700 kA/m is mounted on the rotor of the MEMS USM by adhesives. The printed circuit board is designed to supply the power for the TMR sensor and transmit the digital output to a computer for data recording. The printed circuit board with the TMR sensor is mounted on a frame fixed on a high-precision positioning stage. This positioning stage can ensure that the center of the TMR sensor is aligned with that of the below PMAD and adjusts the distance from the TMR sensor to the PMAD. To calibrate the rotation-measuring system, the baseboard of the MEMS USM has adhered to the center of the HPSM, which can supply a high-precision rotational angle as low as 0.01°. Additionally, the high-precision encoder in the HPSM can output the rotational angle in real time.
In this paper, two testing modes are implemented, which are called the calibrating mode and continuous testing mode, respectively.
In the calibrating mode, the MEMS USM itself is powered off, but the HPSM is powered on. Thus, the rotation of the PMAD is actuated by the HPSM in the calibrating mode, and then the output of the rotation-measuring system changes along with the rotation of the PMAD. Because the exact rotational angles are known from the high-precision encoder of the HPSM, the relationship between the output of the rotation-measuring system and the input rotational angle can be calibrated.
In the continuous testing mode, the MEMS USM itself is powered on, but the HPSM is powered off. As a result, the driving voltage is input into the MEMS USM to make the PMAD rotate continuously. Then, the continuous rotation of the PMAD can be measured. The exact rotational angles are unknown in continuous testing mode. Thus, to obtain the rotational angle, the recorded outputs of the rotation-measuring system are converted into angles using the output–angle relationship acquired in the calibrating mode.
6. Conclusions
This study proposed a rotation-measuring system for the millimeter-scale MEMS USM using TMR sensors for the first time. A PMAD with a radial magnetization of 1700 kA/m is attached to the rotor to satisfy the operating range of the TMR sensor and optimal preload for frictional driving. The calibration based on the HPSM shows that the relationship between the output and rotational angle is highly linear and immune to the rotor’s out-of-plane movement. After the calibration, the continuous rotation of the MEMS USM is tested. It is found that the angle derived from the rotation-measuring system’s output varies periodically, indicating that the measuring system has successfully detected the rotation of MEMS USM. The angle-detecting resolution of the rotation-measuring system is higher than 0.1° and is mainly constrained by the resolution of the TMR sensor. Overall, the rotation-measuring system has the advantages of high resolution, high linearity, and low cost.
In the future, it will be necessary to adopt a calibrating method with higher precision, such as using a high-speed camera, to suppress the calibration error. It is valuable to study the correction method for the nonlinear error. Additionally, it is valuable to study the servo control system based on the rotation-measuring system using the TMR sensor.